Title : The Bansal neuron model: A nonlinear framework for exploring neuronal excitability and electrophysiological dysfunction in Alzheimer's disease
Abstract:
Alzheimer's disease is a progressive neurodegenerative disorder associated with cognitive decline, memory impairment, synaptic dysfunction, and disturbances in neuronal communication. Although amyloid-beta accumulation, tau pathology, neuroinflammation, and neuronal degeneration are recognized components of Alzheimer's disease, understanding how these processes alter electrical excitability remains an important computational challenge. Changes in membrane properties, ionic conductance, synaptic activity, and neuronal response stability may contribute to impaired information processing during disease progression. I propose the Bansal Neuron Model as a mathematical framework for investigating these electrophysiological alterations and their possible relationships to Alzheimer's dementia. This study aims to establish a nonlinear, multiphysics representation of neuronal electrophysiology that can support future investigations of Alzheimer's-related dysfunction. Particular attention is given to membrane charge recovery, voltage-dependent ionic kinetics, delayed electrical relaxation, multi-resonant dynamics, and computational stability. The objective is to distinguish the contributions of individual mechanisms rather than attribute every altered neuronal response to a single pathological process. The Bansal Neuron Model integrates nonlinear membrane charge dynamics with established Hodgkin–Huxley ionic kinetics and additional passive electrical states. Its mathematical organization incorporates the Bansal F1–F5 foundation architectures. Field-derived terminal charge determines differential membrane capacitance, while relaxation and resonant branches introduce independently controllable temporal mechanisms. The framework preserves an exact classical Hodgkin–Huxley restriction, enabling controlled comparisons with established neuronal dynamics. Twelve matched configurations examine constant versus nonlinear field-derived membrane storage, the presence or absence of electrical relaxation, and zero, one, or two resonant branches. In the reported synthetic simulations, a 200-millisecond current stimulus produces fourteen accepted spikes in both the classical reference and the complete nine-state realization. However, first-spike latency changes from approximately 1.901 to 2.121 milliseconds. Local stability analysis identifies corresponding Hopf crossings near 9.775 and 11.111 microamperes per square centimetre. Nineteen operational response protocols further investigate electrophysiological signatures, with nine positive family-level outcomes, nine negative outcomes, and one indeterminate classification.
These computational findings provide a basis for designing future investigations of abnormal neuronal excitability, altered membrane charging, delayed recovery, and frequency-dependent electrical responses in Alzheimer's disease. Disease-associated perturbations could subsequently be informed by experimental electrophysiological recordings and independently established pathological measurements.
The principal contribution of Bansal Neuron Model in Alzheimer's disease research is the explicit coupling and mechanism-resolved evaluation of membrane charge, ionic activity, electrical relaxation, and multi-resonant dynamics. The proposed Alzheimer's-focused investigation considers amyloid-β accumulation, tau pathology, calcium dysregulation, synaptic dysfunction, and oxidative-inflammatory stress as candidate biological perturbations influencing membrane charge, ionic activity, neuronal relaxation, and electrophysiological stability.
Future investigations will extend the Bansal Neuron Model to Alzheimer's disease and dementia by examining disease-associated changes in neuronal excitability, membrane charge dynamics, electrophysiological stability, and impaired neuronal signalling.
Keywords: Bansal Neuron Model; Alzheimer's Disease; Alzheimer's Dementia; Neurodegeneration; Neuronal Electrophysiology; Nonlinear Dynamics; Multiphysics Modelling; Membrane Capacitance; Multi-Resonant Dynamics; Computational Neuroscience
